Problem 1E: Five partners (P1,P2,P3,P4, andP5) jointly own the Gaussian Electric Company. P1 owns 15 shares of... Problem 2E: Five partners (P1,P2,P3,P4, andP5) jointly own the Euler Moving Company. P1 owns 30, P2 owns 25, P3... Problem 3E Problem 4E Problem 5E: In each of the following weighted voting systems, determine which players, if any, have veto power.... Problem 6E: In each of the following weighted voting systems, determine which players, if any, have veto power.... Problem 7E: Consider the weighted voting system[q:7,5,3]. Find the smallest value of q for which a. all three... Problem 8E: Consider the weighted voting system [q:10,8,6,4,2]. Find the smallest value of q for which a. all... Problem 9E: A committee has four members (P1,P2,P3,andP4). In this committee P1 has twice as many votes as P2;... Problem 10E: A committee has six members (P1,P2,P3,P4,P5,andP6). In this committee P1 has twice as many votes as... Problem 11E: Consider the weighted voting system [q:7,5,3]. a. What is the weight of the coalition formed by P1... Problem 12E: Consider the weighted voting system [q:10,8,6,4,2]. a. What is the weight of the coalition formed by... Problem 13E: Find the Banzhaf power distribution of a weighted voting system with four players in which the... Problem 14E: Find the Banzhaf power distribution of a weighted voting system with five players in which the... Problem 15E: Consider the weighted voting system [10:6,5,4,2]. a.Which players are critical in the winning... Problem 16E: Consider the weighted voting system [5:3,2,1,1]. a.Which players are critical in the winning... Problem 17E: a.Find the Banzhaf power distribution of this weighted voting system [6:5,2,1]. b.Find the Banzhaf... Problem 18E: a. Find the Banzhaf power distribution of the weighted voting system [7:5,2,1]. b. Find the Banzhaf... Problem 19E: Consider the weighted voting system [q:5,4,3,2,1]. Find the Banzaf power distribution of this... Problem 20E: Consider the weighted voting system [q:8,4,2,1]. Find the Banzaf power distribution of this weighted... Problem 21E: In a weighted voting system with three players the winning coalitions... Problem 22E: In a weighted voting system with four players the winning coalitions are: {P1,P2}, {P1,P2,P3},... Problem 23E: The Nassau County N.Y. Board of Supervisors 1960s version. In the 1960s, the voting in the Nassau... Problem 24E: The Nassau County N.Y. Board of Supervisors 1960s version. In the 1960s, the voting in the Nassau... Problem 25E: A law firm is run by four partners (A,B,C,andD). Each partner has one vote and decisions are made by... Problem 26E: A law firm is run by four partners (A,B,C,andD). Each partner has one vote and decisions are made by... Problem 27E: Table 2-13 shows the 24 sequential coalitions with pivotal players underlined in a weighted voting... Problem 28E: Table 2-14 shows the 24 sequential coalitions with pivotal players underlined in a weighted voting... Problem 29E: Consider the weighted voting system [16:9,8,7]. a. Write down all the sequential coalitions, and in... Problem 30E: Consider the weighted voting system [8:7,6,2]. a. Write down all the sequential coalitions, and in... Problem 31E: Find the Shapley-Shubik power distribution of each of the following weighted voting systems. a.... Problem 32E: Find the Shapley-Shubik power distribution of each of the following weighted voting systems.... Problem 33E: Find the Shapley-Shubik power distribution of each of the following weighted voting systems.... Problem 34E: Find the Shapley-Shubik power distribution of each of the following weighted voting systems.... Problem 35E: In a weighted voting system with three players the winning coalitions are: {P1,P2}, {P1,P3}, and... Problem 36E: In a weighted voting system with three players the winning coalitions are: {P1,P2}, and {P1,P2,P3}.... Problem 37E: Table 2-15 shows the 24 sequential coalitions in a weighted voting system with four players. In some... Problem 38E: Table 2-16 shows the 24 sequential coalitions in a weighted voting system with four players. In some... Problem 39E: Let A be a set with 10 elements. a. Find the number of subsets of A. b. Find the number of subsets... Problem 40E Problem 41E: For a weighted voting system with 10 players. a. Find the total number of coalitions. b. Find the... Problem 42E: Consider a weighted voting system with 12 players. a. Find the total number of coalitions in this... Problem 43E: Consider a weighted voting system with six players P1 through P6. a. Find the total number of... Problem 44E: Consider a weighted voting system with five players P1 through P5. a. Find the total number of... Problem 45E: Use a calculator to compute each of the following. a. 13! b. 18! c. 25! d. Suppose that you have a... Problem 46E Problem 47E Problem 48E Problem 49E: The purpose of Exercises 49 and 50 is for you to learn how to numerically manipulate factorials. If... Problem 50E: The purpose of Exercises 49 and 50 is for you to learn how to numerically manipulate factorials. If... Problem 51E: Consider a weighted voting system with seven players (P1throughP7). a. Find the number of sequential... Problem 52E: Consider a weighted voting system with seven players (P1throughP6). a. Find the number of sequential... Problem 53E: A law firm has seven partners: a senior partner (P1) with 6 votes and six junior partners... Problem 54E: A law firm has six partners: a senior partner (P1) with 5 votes and five junior partners... Problem 55E Problem 56E Problem 57E: Consider the weighted voting system [q:8,4,1]. a. What are the possible values of q? b. Which values... Problem 58E: Consider the weighted voting system [9:w,5,2,1]. a. What are the possible values of w? b. Which... Problem 59E: Equivalent voting systems. Two weighted voting systems are equivalent if they have the same number... Problem 60E: Veto power. A player P with weight w is said to have veto power if and only if wq, and Vwq Where V... Problem 61E: Consider the generic weighted voting system [q:w1,w2,...,wN]. Assume w1w2...wN. a. Find all the... Problem 62E Problem 63E Problem 64E: The weighted voting system [27:10,8,6,4,2] represents a partnership among five people P1, P2, P3, P4... Problem 65E Problem 66E: Mergers. Sometimes in a weighted voting system two or more players decide to merge-that is to say,... Problem 67E: a.Verify that the weighted voting systems [12:7,4,3,2] and [24:14,8,6,4] result in exactly the same... Problem 68E Problem 69E Problem 70E Problem 71E Problem 72E Problem 73E Problem 74E Problem 75E Problem 76E Problem 77E Problem 78E: Suppose that in a weighted voting system there is a player A who hates another player P so much that... Problem 79E: a. Give an example of a weighted voting system with four players and such that the Shapley-Shubik... Problem 80E: a. Explain why in any weighted voting system with N players a player with veto power must have a... format_list_bulleted
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